1. Field
The exemplary embodiments generally relate to robotic manipulators and, more particularly, to a method and means for the generation of smooth time-optimal trajectories for robotic manipulators.
2. Brief Description of Related Developments
Trajectory generation is typically used when transferring substrates held by a robotic manipulator from one place to another. While robotic systems for carrying light payloads can be over-designed to provide necessary torque margins, increased peak torque requirements become a factor for performance, size, cost and life of both direct-drive and harmonic-drive robotic manipulators for high or heavy payloads. Conventional trajectory generation methods generally do not account for torque constraints or do not produce a smooth commanded trajectory. For example, a well known servo control approach can be found in the paper entitled “Time-optimal control of robotic manipulators along specified paths” from Bobrow et al. (International Journal of Robotic Research, Vol. 4, No. 3, 1985), which generally operates to establish switching points between acceleration and deceleration of a robot end effector without exceeding a maximum tolerable velocity. The switching points generally operate to change the system state in minimum time while at all times using all available system power. This approach is sometimes also referred to as bang-bang control.
While time-optimal, some real world applications can limit the viability of this approach due to the presence of variable or unquantifiable system resonances. More particularly, abrupt changes in jerk (change in acceleration with respect to time) can serve as a broad spectrum excitation of the system, resulting in unacceptably long settle times at the final position.
Conventional systems to remove discontinuities in trajectories from bang-bang control, such as Bobrow et al., by constraining trajectory profiles or kinematic characteristics of the trajectory profiles such as acceleration, jerk and jerk rate result in non-optimal trajectories and hence lower efficiencies. This is especially so for robotic systems configured to handle large, heavier payloads.
It would be advantageous to provide trajectory generation that, e.g., uses maximum system torque and payload accelerations and provides smooth command time-optimal trajectories.